Modelling population redistribution in a leaf beetle: an evaluation of alternative dispersal functions.

1. Dispersal is a fundamental ecological process, so spatial models require realistic dispersal kernels. We compare five different forms for the dispersal kernel of the tansy beetle Chrysolina graminis moving between patches of its host-plant (tansy Tanacetum vulgare) in a riparian landscape. 2. Multi-patch mark-recapture data were collected every 2 weeks over 2 years within a large network of patches and from 2226 beetles. Dispersal was common (28.4% of 880 recaptures after a fortnight) and was more likely over longer intervals, out of small patches, for females and during flooding. Interpatch movement rates did not differ between years and exhibited no density dependence. Dispersal distances were similar for males and females, in both years and over all intervals, with a median dispersal distance of just 9.8 m, although a maximum of 856 m was recorded. 3. A model of dispersal, where patches competed for dispersers based on their size and distance from the beetle's source patch (scaled by the dispersal kernel) was fitted to the field data with a maximum likelihood procedure and each of five alternative kernels. The best fitting had relatively extended tails of long-distance dispersal, while Gaussian and negative exponential kernels performed worst. 4. The model suggests that females disperse more commonly than males and that both are strongly attracted to large patches but do not differ between years, which are consistent with the empirical results. Model-predicted emigration and immigration rates and dispersal phenologies match those observed, suggesting that the model captured the major drivers of tansy beetle dispersal. 5. Although negative exponential and Gaussian kernels are widely used for their simplicity, we suggest that these should not be the models of automatic choice, and that fat-tailed kernels with relatively higher proportions of long-distance dispersal may be more realistic.